Generalized Gauge Theories and Weinberg-Salam Model with Dirac-K\"ahler Fermions

TL;DR

This paper develops a generalized gauge theory framework incorporating Dirac-K"ahler fermions and formulates the Weinberg-Salam model within this context, connecting noncommutative geometry with gauge theories.

Contribution

It introduces a unified formulation of gauge fields and fermions using differential forms, extending previous models to include the Weinberg-Salam model via graded Lie algebras.

Findings

Formulated gauge theories with differential forms of all degrees.

Connected noncommutative geometry to the Weinberg-Salam model.

Demonstrated the model's consistency with known gauge theories.

Abstract

We extend previously proposed generalized gauge theory formulation of Chern-Simons type and topological Yang-Mills type actions into Yang-Mills type actions. We formulate gauge fields and Dirac-K\"ahler matter fermions by all degrees of differential forms. The simplest version of the model which includes only zero and one form gauge fields accommodated with the graded Lie algebra of $SU(2|1)$ supergroup leads Weinberg-Salam model. Thus the Weinberg-Salam model formulated by noncommutative geometry is a particular example of the present formulation.